Darcy Weisbach, ELM & Relative Viscosity
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1 Darcy Weisbach, ELM & Relative Viscosity Dr.ir. Sape A. Miedema Head of Studies MSc Offshore & Dredging Engineering & Marine Technology Associate Professor of Dredging Engineering Faculty of 3mE Faculty CiTG Offshore & Dredging Engineering
2 Dredging A Way Of Life
3 Offshore A Way Of Life
4 What is Offshore & Dredging Engineering? Offshore & Dredging Engineering covers everything at sea that does not have the purpose of transporting goods & people and no fishery.
5 Darcy Weisbach
6 Darcy Weisbach L 1 p 2 l l l v ls D p 2 i l p l l v iw g L 2 g D l 2 ls p l ln lo g D 0.9 p R e 3.7 D p R e
7 Labda Moody diagram for the determination of the Darcy Weisbach friction coefficient. The legend shows the relative roughness. S.A.M Moody Diagram 0.08 Moody Diagram Labda Re Laminar Smooth
8 Darcy-Weisbach friction factor λ (-) S.A.M Moody Friction Factor vs. Line Speed Darcy-Weisbach friction factor λ vs. Line speed v ls Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m Dp= m S.A.M Line speed v ls (m/sec) Dp= m Dp= m
9 Darcy-Weisbach friction factor λ (-) S.A.M Moody Friction Factor vs. Pipe Diameter Darcy-Weisbach friction factor λ vs. Pipe diameter D p vls=1.00 m/sec vls=2.00 m/sec vls=3.00 m/sec vls=4.00 m/sec vls=5.00 m/sec vls=6.00 m/sec vls=7.00 m/sec S.A.M Pipe diameter D p (m)
10 Moody Friction Factor Approximation 1 v D l ls p p D r a n g e : ls v r a n g e :
11 Equivalent Liquid Model
12 Equivalent Liquid Model L 1 p 2 m l m v ls D p 2 i m p m m l v g L 2 g D 2 ls l l p l ln lo g D 0.9 p R e 3.7 D p R e
13 Relative Excess Hydraulic Gradient (E rhg ) S.A.M i 1 R C m s d v s l v 2 ls 2 g D p i 1 R C l s d v s E r h g R i m s d i C l v s i l
14 Relative Viscosity
15 Relative Viscosity ν m /ν l (-) S.A.M Relative Viscosity Collected Relative Viscosity Data, From 16 Sources 100 Experiments 10 Fit Line 4 Terms Upper Limit Lower Limit S.A.M Volume Fraction Solids C v (-)
16 Relative Viscosity ν m /ν fl (-) S.A.M Relative Viscosity, Selected Collected Relative Viscosity Data, Reduced Experiments Fit Line 2 Terms Fit Line 3 Terms Fit Line 4 Terms S.A.M Volume Fraction Solids C v (-)
17 Relative Viscosity, Approximation m r C v s E in s te in l C C e m 2 r v s v s l C vs T h o m a s R e la tiv e D y n a m ic V is c o s ity R e la tiv e K in e m a tic V is c o s ity m m m r l l l r
18 Experiments
19 Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect in Pure Liquid Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity Ratio Potential/Kinetic Energy Cv=0.480 Cv=0.450 Cv= Hydraulic gradient i l (-) S.A.M. Dp= m, d=0.20 mm, Rsd=0.46, Cv=0.450, μsf=0.415
20 Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect with Relative Viscosity Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity Ratio Potential/Kinetic Energy Cv=0.480 Cv= Hydraulic gradient i l (-) Cv=0.400 S.A.M. Dp= m, d=0.20 mm, Rsd=0.46, Cv=0.450, μsf=0.415
21 Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect in Pure Liquid Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity Ratio Potential/Kinetic Energy Cv= Hydraulic gradient i l (-) S.A.M. Dp= m, d=0.04 mm, Rsd=4.00, Cv=0.240, μsf=0.415
22 Relative excess hydraulic gradient E rhg (-) S.A.M Solids Effect with Relative Viscosity Relative excess hydraulic gradient E rhg vs. Hydraulic gradient i l Fixed Bed Cvs=c Sliding Bed Cvs=c. Mean Heterogeneous Flow Cvs=c. Homogeneous Flow Cvs=Cvt=c. Resulting Erhg curve Cvs=c. Fixed Bed, Sliding Bed & Het. Flow Cvt=c. Fixed Bed, Sliding Bed & Sliding Flow Cvt=c. Limit Deposit Velocity Hydraulic gradient i l (-) Ratio Potential/Kinetic Energy Cv=0.240 S.A.M. Dp= m, d=0.04 mm, Rsd=4.00, Cv=0.240, μsf=0.415
23 Questions?
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